Question 894815
let's take a look at how we derive inverse functions by equation.


if y = 5*x, then you find the inverse qeuation by replacing y with x and x with y and solving for y.


y = 5*x becomes x = 5*y


solve for y to get y = x/5.


the inverse equation of y = 5x is y = x/5.


that's by equation.


now by table.


take the same equation of y = 5x and make a table.


you get:


(x,y) = (1,5), (2,10), (3,15), (4,20), etc.


now replace x with y and replace y with x to get:


(x,y) = (5,1), (10,2), (15,3), (20,4), etc.


the first table gets you the equation of y = 5x.


the second table gets you the equation of y = x/5.


all you do is interchange the x valuea and the y values and you have a table for the inverse equation.


graphically, you would plot the (x,y) points for y = 5x.


for each (x,y) point, you would plot the corresponding point of (y,x).


if you then draw the line y = x on your graph you will see that the points of (y,x) are reflections of the points (x,y) about the line y = x.


here's your graph.


you find the reflected points about the line y = x by drawing a line vertical to that line (represented by y = -x) and then finding the intersection of that vertical line with the reflected lines of y = 5x and y = x/5.


the point of intersection will be interchanged.


(10,2) becomes (2,10) and (-10,-2) becomes (-2,-10) as seen on the graph.



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